Flying into JFK on Monday evening and also leaving out of their same day. It is now supposed to snow and they are saying that area could get 1-3 inches (2.5 to 8 cm) of snow. Who has had experience with this and how often are flights canceled or delayed. From what the weather channel is saying the snow will stop early Monday morning my flight is to arrive Monday at 8pm and then my connecting flight is leaving around midnight.
For JFK, 1–3 inches of snow is totally in the expected range of weather, and they are well-equipped to deal with it. If the snow has ended early on Monday morning, then the runways will be cleared by noon, and the planes for your flights will not have to undergo de-icing.
That said, there can be "chain-reaction" effects when weather delays earlier in the day cause early flights to be delayed, and this backlog of departures/arrivals will then interfere with later flights well after the storm has ended. Since this particular storm is arriving overnight, when there are relatively few flights to be affected, I would not expect this to be a problem either; but if the storm has an effect on your flights, that's probably how it will happen.
If an airline thinks that conditions will be bad enough at a particular airport that a significant number of flights will be cancelled or delayed, they will usually allow you to rebook your travel without a change fee. These announcements are usually posted on a "Travel Advisories" page (or a page with a similar name) on the airline's website. Here's Delta's travel advisories page, for example. Google "[airline] travel advisories" to find the appropriate page, and keep an eye on it.